Anonymity is a form of nonidentifiability which I define as noncoordinatability of traits in a given respect. This definition broadens the concept, freeing it from its primary association with naming. I analyze different ways anonymity can be realized. I also discuss some ethical issues, such as privacy, accountability and other values which anonymity may serve or undermine. My theory can also conceptualize anonymity in information systems where, for example, privacy and accountability are at issue.